For a given gas at 1 atm pressure, rms speed of the molecules is $200 \mathrm{~m} / \mathrm{s}$ at $127^{\circ} \mathrm{C}$. At 2 atm pressure and at $227^{\circ} \mathrm{C}$, the rms speed of the molecules will be:

(D) $100 \sqrt{5} \mathrm{~m} / \mathrm{s}$

(A) $80 \mathrm{~m} / \mathrm{s}$

(B) $80 \sqrt{5} \mathrm{~m} / \mathrm{s}$

(C) $100 \mathrm{~m} / \mathrm{s}$

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Heat & Thermodynamics

For a given gas at 1 atm pressure, rms speed of the molecules is

200 m / s

12 7^{\circ} C

. At 2 atm pressure and at

22 7^{\circ} C

, the rms speed of the molecules will be:

(A) $80 m / s$
(B) $805 m / s$
(C) $100 m / s$
(D) $1005 m / s$ ✓ Correct

Answer: (D)

Solution

The rms speed depends only on temperature,

v_{r m s} \propto T

, and not at all on pressure. Converting,

T_{1} = 400

K and

T_{2} = 500

K, so

\frac{v _{2}}{200} = \frac{500}{400} = \frac{5}{2}

, giving

v_{2} = 200 \times \frac{5}{2} = 1005

m/s.

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Single correct option

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